An Encoding Algorithm of Triply Extended Reed-Solomon Codes With Asymptotically Optimal Complexities

• Published in: IEEE transactions on communications Vol. 66; no. 8; pp. 3235 - 3244
• Main Author: Lin, Sian-Jheng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; algorithm design and anlaysis; Algorithms; Approximation algorithms; Coding; Complexity theory; Computer simulation; Decoding; Encoding; Generators; Lower bounds; parallel processing; Reed-Solomon codes; Scheduling; Scheduling algorithms
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2017.2737441

In this paper, we devise a fast encoding algorithm for triply extended Reed-Solomon codes. The proposed approach requires approximately two XORs per bit, which improves the prior result of three XORs per bit established by certain maximum distance separable (MDS) array codes. We also prove that, for MDS codes with two and three parities, the scheduling algorithms require at least two XORs per bit. To the best of our knowledge, this is the first provable scheduling algorithm for the triple-parity MDS codes to approach the theoretical lower bounds. The implementation with SIMD instructions is provided. The simulations show that the proposed approach is competitive, as compared with other cutting edge implementations.